MTG Finance Fundamentals: Trading, the Zero-Sum Game

Now that I have been writing articles for Red Site Wins for about a month, I would like to introduce myself a little further, so that I am not that androgynous tweeter / article writer who knows a little bit about MTG finance. My name is Sigmund (nickname Sig), and I work for a large consumer goods company in Boston, MA. My wife and I just recently moved here from Cincinnati. Prior to that, I grew up in New Jersey and went to Clarkson University for college, studying Chemical Engineering. In terms of the Magic Universe, I started playing when Visions was the new set. I took a sabbatical from the game during Urza’s block, and played on and off from then until Time Spiral block. It was in Time Spiral block that I really started to play serious Magic.

While I studied at Clarkson University, I decided to take a course in Game Theory, offered by the economics department at the college. The course covered a diverse collection of “games”, defined as any situation where there are multiple people whose decisions impact the outcome of the situation. While not directly related to the game of Magic, there are still a great number of overlapping concepts, especially when the concept of trading is evaluated analytically. But I want to take a step back with this article, and try to apply Game Theory to trading Magic cards. Perhaps by approaching the paradigm in this sense, some light may be shed onto decisions being made and motivations for those decisions.

I would like to introduce the following position: trading Magic cards is a “zero-sum game”. A zero-sum game is a situation in which one participant’s gain is equivalent to the other participant’s loss, and vice versa.

Assumptions

Before proceeding further with the analysis, I must proceed with due diligence and document my assumptions behind this statement. First, both participants must be sane, in the sense that they both want to make the decision that maximizes their outcome. Notice how I used the word outcome here and not value; some people are happier with other benefits from a trade rather than simply making value. I will delve into this topic further in a moment.

My second assumption is that the two participants in the trade are neutrally oriented towards each other. In other words, a trade between two parties with additional agendas may seek a more sophisticated quid pro quo situation beyond simply trading Magic cards. For example, I may be willing to trade away a card and knowingly lose value on it if the card is going to be used that weekend by a pro, and I may get a little recognition from said pro for my charity. Alternatively, if my friend’s cards were stolen, I would gladly trade heavily in his favor to help him back to his feet. These situations involve a more complicated “payout” system involving emotions and ambitions beyond the context of cards; therefore, they will be exceptions to my discussion.

Rationale

From the most simplistic angle, my claim that Magic is a zero-sum game is rather one-dimensional. Still, I want to touch upon it briefly to establish a foundation for my argument. If I trade you a Tarmogoyf for 2x Liliana of the Veil, for example, I am losing a Tarmogoyf and gaining 2 Liliana of the Veil while you are losing the 2 Lilianas and gaining the Tarmogoyf. Without any other factors being considered, there can be no reasonable argument that this is not a zero-sum game. If we were to go our separate ways and sell our cards immediately on eBay, I would likely make 90 – 100$ and my trade partner would likely make around 75$. If I had not made the trade, and we sold the cards on eBay, the payouts would have been switched. As a result from this exchange, my payout was about 25$ on the high end while my trade partner’s would have been -25$. The sum of these two payouts, of course, is zero.

The same scenario has possibly different outcomes should the context be specified. Often times, a trade is made in order to obtain cards needed for a deck. If I was at a SCG tournament and traded someone the Tarmogoyf right before the Sunday legacy tournament, would the payout be any different for each of us? Absolutely it would. That Tarmogoyf may be the 4th that my trade partner needs for his Zoo deck, thereby increasing his chances of winning the tournament. Now his payout, rather than being 25$ in the red, is higher once this added benefit is factored in. It is much more difficult to quantify the added benefit. One could take the potential increase of match win percentage and multiply it by the prize payout of the tournament. For sake of argument, let’s establish the value as 10$. Now, my trade partner’s payout was -15$ rather than -25$.

In the meantime, was my payout equally impacted? Well, if I were playing Zoo and that was my 4th Tarmogoyf, then certainly yes. But if I was playing Reanimator, perhaps, then the argument could be made that I still made 25$. However, this is too simplistic of an analysis. Assuming my trade partner was acting in his best interest, he surely would have traded for the Tarmogoyf at the best value possible. In this scenario, he found someone who would take two copies of a potentially over-hyped standard card for the Tarmogoyf, a long-time legacy staple. Therefore, looking at the exchange neutrally, it’s possible that a value of the Tarmogoyf of 75$ is inaccurate in this context. Perhaps a retail value should be used given the fact that the legacy tournament was about to begin and a legacy card was being traded for a standard card. In this case, I could potentially have traded the Tarmogoyf to someone else for 85$ instead of 75$, which is much closer to retail price. Net, my gained value is impacted negatively by that difference. Consequently, the opportunity cost detracts from my outcome where it was gained by my partners, yielding a net outcome of zero between the two of us (even though long term dollar value may have been uneven). Should the roles have been reversed, the outcomes would have been identical and opposite, further supporting the fact that this was zero-sum once emotion is removed as a factor.

Now, this scenario can be dissected in an array of ways, with extenuating circumstances added on freely in order to invalidate the example. So I will conclude my argument with a generalized perspective which espouses a philosophical view. At the end of the day, an exchange is being made between two parties. These exchanges are being made in a given context, which significantly influences the value of the trade from either side’s vantage point. Still in nearly all scenarios, the roles could easily be reversed (again, assuming the trade partners are neutral towards each other) and payouts would remain identical. Using the previous example, I could just as easily decided to play Zoo that tournament and my opponent Reanimator. And if the trade were in the reverse direction, I would be losing the 15$ value and he gain the 15$. The reason is simple: this is a decision we both can make at any given time.

And extended further, two months later I could really regret having traded that Tarmogoyf. Once I trade away my Tarmogoyf, even if I perceive added value because I am “happy with the trade”, I am still out a Tarmogoyf and my net outcome was impacted by a set amount. And while I still have 2 Liliana of the Veil I can trade towards a Tarmogoyf, it is certainly not the same as having the Tarmogoyf. If Liliana of the Veil was still a 50$ card, this would be easy (and note I would have made out well on the trade). If not, then the trade was not as strongly in my favor. In either case, the outcome would be opposite for my trade partner, with net outcomes adding to zero. Therefore, I insist that in the long run, regardless of who was “happy with the trade”, trading is a zero sum game with a winner and loser.

Author’s Note:

This does not mean you should only proceed with trades where you feel you are the winner; this will be difficult because emotion easily confounds things. In fact, the best traders I know are able to remove emotion from the equation. They can trade a piece of power away for thousands of bulk rares, simply because they know they are winning in the zero-sum game by acquiring cards they can sell for cash and use that cash to buy the Mox back, with money left over. Now, time is certainly a factor worth considering, but this can also be added to (or subtracted from) one’s outcome. Regardless, the net of the trade is zero. Like matter, value cannot be created or destroyed, only changed.